Cviceni1.tex

\documentclass[]{article}

\usepackage{fontspec}

\usepackage{tikz}
\usetikzlibrary{intersections}

\begin{document}
	\begin{tikzpicture}
		[scale=3,line cap=round,
		axes/.style=,
		important line/.style={very thick},
		information text/.style={rounded corners,fill=red!10,inner sep=1ex}]
		
		\def\costhirty{0.8660256}
		
		\colorlet{anglecolor}{green!50!black}
		\colorlet{sincolor}{red}
		\colorlet{tancolor}{orange!80!black}
		\colorlet{coscolor}{blue}
		
		\draw[help lines,step=0.5cm] (-1.4,-1.4) grid (1.4,1.4);
		
		\draw (0,0) circle (1cm);
		
		\begin{scope}[axes]
			\draw[->] (-1.5,0) -- (1.5,0) node[right] {$x$} coordinate (x axis);
			\draw[->] (0,-1.5) -- (0,1.5) node[above] {$y$} coordinate (y axis);
			
			\foreach \x/\xtext in {-1, -.5/-\frac{1}{2}, 1}
				\draw[xshift=\x cm] (0pt,1pt) -- (0pt,-1pt) node[below,fill=white] {$\xtext$};
			
			\foreach \y/\ytext in {-1, -.5/-\frac{1}{2}, .5/\frac{1}{2}, 1}
				\draw[yshift=\y cm] (1pt,0pt) -- (-1pt,0pt) node[left,fill=white] {$\ytext$};
			
			\filldraw[fill=green!20,draw=anglecolor] (0,0) -- (3mm,0pt) arc (0:30:3mm);
			\draw (15:2mm) node[anglecolor] {$\alpha$};
			
			\draw[important line,sincolor]
				(30:1cm) -- node[left=1pt,fill=white] {$\sin \alpha$} (30:1cm |- x axis);
			
			\draw[important line,coscolor]
				(30:1cm |- x axis) -- node[below=2pt,fill=white] {$\cos \alpha$} (0,0);
			
			\path [name path=upward line] (1,0) -- (1,1);
			\path [name path=sloped line] (0,0) -- (30:1.5cm);
			\draw [name intersections={of=upward line and sloped line, by=t}]
				[very thick,orange] (1,0) -- node[right=1pt,fill=white]
				{$\displaystyle \tan \alpha \color{black}=
				\frac{{\color{red}\sin \alpha}}{\color{blue}\cos \alpha}$} (t);
			
			\draw (0,0) -- (t);
			
			\draw[xshift=-1.075cm,yshift=-2.1cm]
				node[right,text width=6cm,information text] {
				The {\color{anglecolor} angle $\alpha$} is $30^\circ$ in the
				example ($\pi/6$ in radians). The {\color{sincolor}sine of
				$\alpha$}, which is the height of the red line, is
				\[
				{\color{sincolor} \sin \alpha} = 1/2.
				\]
				By the Theorem of Pythagoras…
				};
		\end{scope}
	\end{tikzpicture}
\end{document}